In Exercises 35–54, use the FOIL method to multiply the binomials...

Question

In Exercises 35–54, use the FOIL method to multiply the binomials.

(x+5)(x+8)

Accepted Answer

Hey, everyone. Welcome back. Using the foil method of multiplication. What is the product of the following binomials? The first binomial we're given is H-plus six and that's multiplied by the second binomial H plus nine. We're given four answer choices. Option A H squared plus 50 4h plus 15. Option B H squared plus 15 H plus 54. Option C H squared plus three H plus 54 and option DH squared plus 50 4h plus three. We're gonna start by rewriting our binomials. So we have the binomial H plus six multiplied by the binomial H plus nine. And what the foil method tells us tells us to take the first term of the first binomial, first term of the second binomial and multiply them together. OK. Then it tells us to take the outside terms multiply them together, the inside terms multiply them together. And the last terms multiply them together. And that gives us the four terms of our resulting expression first, outside inside last. So if we apply this to our expression, we start with the first terms. So the first term of the first expression is H the first term of the second expression is H, so we have H multiplied by H which represents our first terms or the F in foil, then we're going to add the next term and that's gonna come from the outside. OK. So we're gonna take the outermost term. So the far left and the far, right, in our expression, on the far left, we have an outside term of H and on the far right, we have an outside term of nine. So we get H multiplied by nine, which gives us our outside term. Now we do the same for the inside. So we're going to add Our inside term and the inside term, we take the two tightest inside terms that touch each other almost. So we have from the first term sticks multiplied by the second term H so six multiplied by H is our inside term, maybe I in foil. And then we're gonna add our last term. OK. So we're gonna take the last term from our first binomial six And we're gonna multiply the last term of the second binomial nine. So we have six multiplied by nine. And this is our last terms for the L in foil. So now we have the first outside inside last foil. So this is, we've applied the method. Now we've done the multiplication and what's left to do is just simplify. So we have H multiplied by H recall when we have two things with the same base multiplied together we add the exponents, so we get H to the exponent one plus one. Then we're gonna add our next term. We have h multiplied by nine. We can write this as nine h. Uh We add six multiplied by H So six h And we add six multiplied by 9:54. Now, we're almost there. We have a little bit of simplifying. We can do OK, we can simplify the exponent in this first term. And also notice that we have two terms that have H OK. So we can combine those into one term. So we have H to the exponent one plus one gives us H squared. We have nine H plus six H, we can combine these to 15 H. So we have H squared plus 15 H plus our constant term 54. So now we have a single H squared term, a single H term and a constant term. So this is as simple as we can make our expression. And this is what we were looking for. If we compare this to our answer choices, we found that using the foil method, the product of these binomials is H squared plus 15 H plus 54 which corresponds with answer choice B. That's it for this one. Thanks everyone for watching. See you in the next video.

In Exercises 35–54, use the FOIL method to multiply the binomials. (x+5)(x+8)

Concetti chiave

Binomials

FOIL Method

Distributive Property

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